1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. 1. The length of a wall is 4 ft more than three times the height.
Warm Up
Write an equation for each function. Tell what each variable you use represents.
1. The length of a wall is 4 ft more than three times the height.
2. The number of trading cards is 3 less than the number of buttons.
l = 3h + 4, where l is length and h is height.
c = b – 3, where c is the number of cards and b is the number of buttons.

3. Problem of the Day
Steve saved $1.50 each week. How many weeks did it take him to save enough to buy a $45 skateboard? 30

4. Sunshine State Standards
MA.6.A.3.6 Construct and analyze tables, graphs, and equations to describe linear functions…using…algebraic notation.
Also MA.6.A.3.2

5. Vocabulary
linear equation

6. Additional Example 1: Finding Solutions of Equations with Two Variables
Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x = 1, 2, 3, 4.
Make a function table by using the given values for x to find values for y.
Write these solutions as ordered pairs.
(x, y)‏ 18
4(4) + 2 4 14
4(3) + 2 3 10
4(2) + 2 2 6
4(1) + 2 1 y
4x + 2 x
(1, 6)‏
(2, 10)‏
(3, 14)‏
(4, 18)‏

7. Check It Out: Example 1
Use the given x-values to write solutions of the equation y = 5x + 3 as ordered pairs. x = 2, 3, 4. 23
5(4) + 3 4 18
5(3) + 3 3 13
5(2) + 3 2
(x, y)
5x + 3 x
(2, 13)‏
(3, 18)‏
(4, 23)‏ y

8. Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.

9. Additional Example 2: Checking Solutions of Equations with Two Variables
Determine whether the ordered pair is a solution to the given equation.
(3, 21); y = 7x
Write the equation.
y = 7x
21 = 7(3)‏ ?
Substitute 3 for x and 21 for y.
21 = 21 ? 
So (3, 21) is a solution to y = 7x.

10. Check It Out: Example 2A
Determine whether the ordered pair is a solution to the given equation.
(4, 20); y = 5x
y = 5x
20 = 5(4)‏ ?
20 = 20
(4, 20) is a solution to y = 5x.

11. Check It Out: Example 2B
Determine whether the ordered pair is a solution to the given equation.
(2, 3); y = x + 1
y = x + 1
3 = 2 + 1 ?
3 = 3
(2, 3) is a solution to y = x + 1.

12. (6, 4) is not a solution to y = 2x - 7.
Check It Out: Example 2C
Determine whether the ordered pair is a solution to the given equation.
(6, 4); y = 2x - 7
y = 2 x – 7
4 = 2(6) - 7‏ ?
4 = 5
(6, 4) is not a solution to y = 2x - 7.

13. Check It Out: Example 2D
Determine whether the ordered pair is a solution to the given equation.
(5, 1); y = 3x - 12
y = 3x - 12
1 = 3(5)‏ - 12 ?
1 = 3
(5, 1) is a solution to y = 3x - 12.

14. You can also graph the solutions of an equation on a coordinate plane
You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs of some functions, they form a straight line. The equations that express these functions are called linear equations.

15. Additional Example 3: Reading Solutions on Graphs
Use the graph of the linear function to find the value of y for the given value of x.
x = 4
Start at the origin and move 4 units right. x y 4
Move up until you reach the graph. Move left to find the y-value on the y-axis. 2 -2
When x = 4, y = 2.
The ordered pair is (4, 2). -4

16. Check It Out: Example 3A
For each graph of a linear function, find the values of y for the values of x given below the graph.
x = 2 y 2 x 9 8 7 6 5 1 3 4 10
y = 6

17. Check It Out: Example 3B
For each graph of a linear function, find the values of y for the values of x given below the graph.
x = 0 y 2 x 9 8 7 6 5 1 3 4 10
y = 9

18. Check It Out: Example 3C
For each graph of a linear function, find the values of y for the values of x given below the graph.
x = 4 y 2 x 9 8 7 6 5 1 3 4 10
y = 3

19. Check It Out: Example 3D
For each graph of a linear function, find the values of y for the values of x given below the graph.
x = 1 y 2 x 9 8 7 6 5 1 3 4 10
y = 6

20. Check It Out: Example 3E
For each graph of a linear function, find the values of y for the values of x given below the graph.
x = 4 y 2 x 9 8 7 6 5 1 3 4 10
y = 7

21. Check It Out: Example 3F
For each graph of a linear function, find the values of y for the values of x given below the graph.
x = 7 y 2 x 9 8 7 6 5 1 3 4 10
y = 8

22. Additional Example 4: Graphing Linear Functions
Graph the function described by the equation. y = 3x+ 2 8
3(2) + 2 2 5
3(1) + 2 1
3(0) + 2 y
3x + 2 x
(0, 2)‏
(1, 5)‏
(2, 8)‏

23. Additional Example 4 Continuedy x 9 8 7 6 5 1 3 4 2

24. Check it out : Example 4A
Graph the function described by the equation. y = x + 3 5
(2) + 3 2 4
(1) + 3 1 3
(0) + 3 y
x + 3 x
(0, 3)‏
(1, 4)‏
(2, 5)‏

25. Check it out : Example 4A Continuedy 2 x 9 8 7 6 5 1 3 4

26. Graph the function described by the equation. y = 2x + 5
Check it out : Example 4B
Graph the function described by the equation. y = 2x + 5 9
2(2) + 5 2 7
2(1) + 5 1 5
2(0) + 5 y
2x + 5 x
(0, 5)‏
(1, 7)‏
(2, 9)‏ 8 6 3 4 10

27. Graph the function described by the equation. y = 3x + 3
Check it out : Example 4C
Graph the function described by the equation. y = 3x + 3 9
3(2) + 3 2 6
3(1) + 3 1 3
3(0) + 3 y
3x + 3 x
(0, 3)‏
(1, 6)‏
(2, 9)‏ 8 7 5 4 10

28. Graph the function described by the equation. y = 8 - x
Check it out : Example 4D
Graph the function described by the equation. y = 8 - x 2
8 - 6 6 1
8 - 7 7
8 - 8 8 y
8 - x x
(8, 0)‏
(7, 1)‏
(6, 2)‏ 9 5 3 4 10

29. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 29 29

30. Lesson Quiz
1. Use the given x-values to write solutions as ordered pairs to the equation y = 10x + 5 for x = 0, 1, 2, and 3.
2. Determine whether (4, 2) is a solution to the equation y = 5x – 6.
(0, 5), (1, 15), (2, 25), (3, 35‏)
No, 2 ≠ 5(4) – 6

31. 3. Graph the function described by the equation y = 5 – x.
Lesson Quiz Cont.
3. Graph the function described by the equation y = 5 – x. y x 9 8 7 6 5 1 3 4 2

32. Lesson Quiz for Student Response Systems
1. Use the given x-values to identify solutions as ordered pairs to the equation y = –7x + 4 for x = 1, 3, 5, and 7.
A. (1, 11), (3, 25), (5, 39), (7, 53)
B. (1, 3), (3, 17), (5, 31), (7, 45)
C. (1, –11), (3, –25), (5, –39), (7, –53)
D. (1, –3), (3, –17), (5, –31), (7, –45) 32 32

33. Lesson Quiz for Student Response Systems
2. Identify the graph of the function described by the equation y = x – 5.
A B. 33 33